Bio-inspired Space Filling Fractal Network Metamaterial

Fractal geometry are prevalent in natural composite materials. Inspired by the complex fractal geometry of deer cranial suture, we introduced the mathematical concept of space-filling fractal curves to describe the pattern formed by a continuously moving point in space. Two space-filling curves, Hillbert and Peano curves, are used to design two-phase mechanical metamaterials. The designs are fabricated via a multi-material 3D printer. Along the space-filling lines, soft rubbery material is used, forming a connected compliant layer to provide constrains for the second phase. Outside the soft phase, a hard plastic material is used as the second phase. Mechanical experiments under uniaxial tension are conducted on the specimens. The effect of fractal iteration and the volume fraction of the two phases are systematically quantified. Both analytical and numerical analyses are performed to predict the effective material properties.

Results from these studies demonstrate that the space filling fractal designs with higher fractal iterations show enhanced toughness and fracture resistance. Moreover, these enhanced mechanical properties can be systematically tuned by varying the volume fraction of the soft phase and the fractal iteration. The results provide design guidelines for this novel family of architecture materials with remarkable mechanical performance.